2025 CJC Promo Q8

The diagram shows the curve \(y=\mathrm{f}(x)\). The curve crosses the \(x\)-axis at its minimum point \((-3,0)\).

It has a maximum turning point \((-1,-4)\) and crosses the \(y\)-axis at the point \((0,-4.5)\). The asymptotes of the curve are \(x=-2\) and \(y=-x-4\).

On separate diagrams, sketch the graphs of

1. \(y=\mathrm{f}'(x)\),[3]
2. \(y=\dfrac{1}{\mathrm{f}(x)}\),[3]
3. \(y=|\mathrm{f}(x)|\),[3]

indicating the equations of any asymptotes, turning points and intersections with the axes.